so what is the difference between the comma and the dashes, don't the both do the same thing?

Dashes are more emphatic. Use commas when the text between them is a "normal" part of the sentence, with neither more nor less emphasis than the rest of it. Use dashes when you want to make the text enclosed between them more emphatic than the rest of the sentence. Similarly, use parentheses when the enclosed text has less emphasis; think of what's in parentheses as being an "aside" to the reader.

Eg, compare:

He drove the car (very quickly) along the road.
He drove the car, very quickly, along the road.
He drove the car--very quickly--along the road.

The "very quickly" goes from "low emphasis" to "high emphasis" between these sentences.

If you take the commas out and use en or em dashes it will accept it because the construction - although still clumsy - is now valid.

Depends upon whose grammar you're using, I guess. The only one I can remember dashes being taught at all was the hyphen, which had a caveat that you should use as few as possible. AKA none.

This was repeated in the 1996 Little,Brown Handbook (which I took great pleasure in burning when I got out of high school). No dashes, just hyphens. Parentheses were also right out, because the MLA has reserved them for parenthetical citation.

Either way, IMO the Word grammar checker just doesn't like complex sentences.

Sometimes though on one of those complicated sentences that we were taught not to use, with danglers, descenders, ascenders, gerunds, et. al., and we have gotten caught up in the moment and wish to tough it out rather than using the KISS rule, and the wife is busy, I might try the grammar checker to see if it brings an insight.

I tried it and it did pick up on the many, many occasions where I'd missed out a comma, but at the same time it was extremely slow in a large document and I was writing a lot of dialogue in Scottish dialect which messed with it a bit.

I'd suggest finding a good beta reader if you can. You can highlight a few of the phrases you're worried about for them to cast an eye over. Or, bite the bullet and go for an editor. They might pick up on consistent problems with your style which would make you a better writer overall. It's just soooo expensive!

I wouldn't trust a grammar checker too much, anymore than I'd rely on a spellchecker to find and fix all my mistakes. It's not a bad thing to use either, but a lot of the time it will come back to what you know about writing and what you're trying to do.

That's especially true for fiction writing, which may tend toward being informal or purposefully "wrong" for effect. For a formal writing project, like a business report, it might be a lot more useful.

Now, if I could find something that would read my mind and automatically insert commas for me, that would be really great!